$A$ and $B$ are two events such that $P(A)=0.54$,$P(B)=0.69$ and $P(A \cap B)=0.35$. Find $P(A \cap B^{\prime})$.

Let $E_{1}, E_{2}, E_{3}$ be three mutually exclusive events such that $P(E_{1}) = \frac{2+3p}{6}$,$P(E_{2}) = \frac{2-p}{8}$,and $P(E_{3}) = \frac{1-p}{2}$. If the maximum and minimum values of $p$ are $p_{1}$ and $p_{2}$,then $(p_{1} + p_{2})$ is equal to.

$2$ boys and $2$ girls are in Room $X$,and $1$ boy and $3$ girls are in Room $Y$. Specify the sample space for the experiment in which a room is selected and then a person.

If the events $A$ and $B$ are independent,and $P(A^{\prime}) = \frac{2}{3}$ and $P(B^{\prime}) = \frac{2}{7}$,then $P(A \cap B)$ is equal to:

$A$ card is drawn at random from a pack of $52$ cards. What is the probability that the drawn card is neither a heart nor a king?

The probabilities that $A$ and $B$ will die within a year are $p$ and $q$ respectively. Then,the probability that only one of them will be alive at the end of the year is